Re: Idempotence and "Replication Insensitivity" are equivalent ?

pamelafluente_at_libero.it wrote:
> vc ha scritto:
> > Earlier, I said that the sample median regarded as an interval (50
> > percentile) *is* invariant under monotone transformations.
>
> Ok let's assume that there exists such a thing like a "sample median
> regarded as an interval " (it's not a correct expression but I
> understand that you want to mean the interval of values which minimizes
> the sum of absolute deviations), then you have to define what you mean
> by "invariance", as the definition you provided:
>
> m(f(X)) = f(m(X)).
>
> does not apply to intervals.

I am sorry, I did not realize that you did not understand the above
elementary notation. As I said before let 'X' be a real-valued random
variable, ' f' a transformation function and 'm' the function mapping
the r.v. to a set possibly but not necessarily consisting of a single
element and representing the median. Using the function compositionn
notation, one could also write m o f o X = f o m o X (which is not
much different). Does it help ?

> Only after you have provided such a
> definition of invariance, we can check if your statement is ok.
>
> Otherwise, we are left with a sentence that does not make sense : "
> sample(?) median regarded as an interval (50 percentile(?) ) *is*
> invariant under monotone transformations ".